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Measurable Success can be measured by the number of applications, interviews and job offersSection 16 Vector Functions We first saw vector functions back when we were looking at the Equation of LinesIn that section we talked about them because we wrote down the equation of a line in \({\mathbb{R}^3}\) in terms of a vector function (sometimes called a vectorvalued function)In this section we want to look a little closer at them and we also want to look at some vector functionsDefinition In the case of a space curve, the radius of curvature is the length of the curvature vector In the case of a plane curve, then R is the absolute value of ≡ =, where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature Formula In 2D If the curve is given in Cartesian coordinates as y(x), then the radius of curvature is
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Y=a(1+r)^t examples
Y=a(1+r)^t examples-The characteristic equation is r2 5 r 4 = (r 1)(r 4) = 0, the roots of the polynomial are r = −1 and −4 The general solution is then y = C1 e −t C 2 e −4t Suppose there are initial conditions y(0) = 1, y′(0) = −7 A unique particular solution can be found by solving for C1 and C2 using the initial conditions First weIn this section we solve linear first order differential equations, ie differential equations in the form y' p(t) y = g(t) We give an in depth overview of the process used to solve this type of differential equation as well as a derivation of the formula needed for the integrating factor used in the solution process
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Y Write the exponential growth function= a(1 r)t = 150,000(1 008)t Substitute 150,000 for a and 008 for r Add= 150,000(108)t The festival attendance can be represented by y = 150,000(108)t b The value t = 4 represents the fi fth year because t = 0 represents the fi rst year y = 150,000(108)t Write the exponential growth function# A formula y ~ x # A converted formula y = a_1 a_2 * x This is an example of a simple conversion y ~ x gets translated into y = a_1 a_2 * x To see and understand what R actually happens, you can use the model_matrix() function This function creates a design or model matrix by, for example, expanding factors to a set of dummy variables, depending on the contrasts, and expanding interactions similarlySpeed, r = 48 miles/hour Step 2
At any point along the path, the (small) tangent vector ${\bf r}'\,\Delta t$ gives an approximation to its motion over a short time $\Delta t$, so the work done during that time is approximately ${\bf F}\cdot{\bf r}'\,\Delta t$;= 1 r Subtracting 1, you get that the rate is just over 003 or 3/10 of 1% The function that would model your growth is y = 484(1003)^t To do #2, find out how many years each year is after 1980, and plug those numbers in for "t" For example, to find 1985, you'd take 484(1003)^5 To do #3, "double" the original population would be 968 million peopleFor t and r must be the same Example of Exponential Growth The 00 census found that a US Population of about 281 million with an estimated growth rate of 07% Q = Q0 x (1 r)t 4/1/10 2 Forms of the Exponential
1 Loop Examples 11 Example Sum Primes Let's say we wanted to sum all 1, 2, and 3 digit prime numbers To accomplish this, we could loop through all 1, 2, and 3 digit integers, testing if each is a prime number (using the isprime function) If and only if a particular value is prime, then we'll add it to our running totalUsing the growth formula we have y = a(1 r) x where a = 1 (we start with 1 bacteria), and r = 100%, since the amount doubles y = 1(1 100) x = 2 x (same result) Notice that the graph is a scatter plot You cannot have a fractional part of a bacteria The dotted line is the exponential function which contains the scatter plots (the model)Example x 0 = 50 r = 4% = 004 t = 90 hours x(t) = x 0 × (1 r) t = 50×(1004) 90 = 1706 Exponent calculator
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Example Example 321 Let R be the relation on the set R real numbers defined by xRy iff x−y is an integer Prove that R is an equivalence relation on R Proof I Reflexive Suppose x ∈ R Then x−x = 0, which is an integer Thus, xRx II Symmetric Suppose x,y ∈ R and xRy Then x − y is an integerEXAMPLE 1 (a) Find the derivative of r(t) = (2 t3)i te−tj sin(6t)k (b) Find the unit tangent vector at the point t = 0 SOLUTION (a) According to this theorem, we differentiate each component of r r'(t) = Correct Your answer is correctMeasurable Success can be measured by the number of applications, interviews and job offers
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Warmup y = a(1r)t 10) 00(1 003)1 = $60 11) 0(1 003)10 = $ 12) 600(1 007)4 =$ 13) 1500(1 004)8 = $5285There is a substantial number of processes for which you can use this exponential growth calculator The general rule of thumb is that the exponential growth formula x(t) = x 0 * (1 r/100) t is used when there is a quantity with an initial value, x 0, that changes over time, t, with a constant rate of change, rThe exponential function appearing in the above formula has a base equal to 1P = C (1 r) t Continuous Compound Interest When interest is compounded continually (ie n > ), the compound interest equation takes the form P = C e rt Demonstration of Various Compounding The following table shows the final principal (P), after t = 1 year, of an account initially with C = $, at 6% interest rate, with the given
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Suppose that the path of an object is given by a vector function ${\bf r}(t)$;61 INTRO TO LINEAR TRANSFORMATION 191 1 Let V,W be two vector spaces Define T V → W as T(v) = 0 for all v ∈ V Then T is a linear transformation, to be called the zero transOneSample ttest The onesample ttest, also known as the singleparameter t test or singlesample ttest, is used to compare the mean of one sample to a known standard (or theoretical / hypothetical) mean Generally, the theoretical mean comes from a previous experiment For example, comparing whether the mean weight of mice differs from 0 mg, a value determined in a previous study
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Exponential Decay Definition And Function
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This equation gives the amount B that the person still needs to repay after t years B = A (1 r/n) NT P (1 r/n) NT 1 (1 r/n) 1 where B = balance after t years A = amount borrowed n = number of payments per year P = amount paid per paymentAnd = 2 2 2 2!Example 12 Find the length of ~r(t) =~it2~j t3~k for 0 6 t 6 1 This is straight forward calculations L = Z 1 0
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Question Use the compound interest formula A=P(1r/n)^nt to answer the following questions In the formula, A is the amount of money in the savings account, P is the principle, r is the interest rate, t is the time that the money is in the account, and n is the number of times the money is compounded per yearPrecalculus Examples Popular Problems Precalculus Solve for t A=P(1r/n)^(nt) Rewrite the equation as Divide each term by and simplify Tap for more steps Divide each term in by Cancel the common factor of Tap for more steps Cancel the common factor Divide byDefinition In the case of a space curve, the radius of curvature is the length of the curvature vector In the case of a plane curve, then R is the absolute value of ≡ =, where s is the arc length from a fixed point on the curve, φ is the tangential angle and κ is the curvature Formula In 2D If the curve is given in Cartesian coordinates as y(x), then the radius of curvature is
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Thieme Chemistry Synthesis Issue 9 Is Online T Co Olfnfq7cal Elena Averina And Co Workers Use Tetranitromethane Triethylamine Or 𝘵 Buono To Synthesize Isoxazoles By Heterocyclization Of Unsaturated Ketones Primary Data Is
Lipschitz condition De nition function f(t;y) satis es a Lipschitz condition in the variable y on a set D ˆR2 if a constant L >0 exists with jf(t;y 1) f(t;y 2)j Ljy 1 y 2j;Example 1 I will obtain a job as a high school math teacher within three months after graduating with my Bachelor of Science in Education Specific The goal of becoming a high school math teacher is welldefined;Examples Let S = ℤ and define R = {(x,y) x and y have the same parity} ie, x and y are either both even or both odd The parity relation is an equivalence relation 1 For any x ∈ ℤ, x has the same parity as itself, so (x,x) ∈ R 2 If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R 3
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9 6 Exponential Growth And Decay Pg 38 Notebook Y Amount Remaining After Growth Or Decay A Initial Amount Of Material T Time The Material Has Ppt Download
Example 1 I will obtain a job as a high school math teacher within three months after graduating with my Bachelor of Science in Education Specific The goal of becoming a high school math teacher is welldefined;Learn termexponentialgrowth = y=a(1r)^t with free interactive flashcards Choose from 500 different sets of termexponentialgrowth = y=a(1r)^t flashcards on Quizlet2 Solution Reading o the coe cients of the parameters t and s, we see that v 1 = i 3j 2k and v 2 = 2i 4j 7k are the direction vectors for L 1 and L 2Because v 1 v 2 = 2 12 14 = 0, we conclude that the lines are perpendicular
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1= p 2 for x= (1;0)T Example of a norm that is not submultiplicative jjAjj mav= max i;j jA i;jj This can be seen as any submultiplicative norm satis es jjjj jjAjj2 In this case, A= 1 1 1 1!To find the interest rate (r) in the formula a=p(1r)^t, you need to know the values of a (amount), p (principal) and t (time) You would take a and divide it by p You will then take that result and take the t root of it You then subtract that answer by 1 to get your interest rate in decimal form Here is an example You need to find the interest rate of an account that grew from $4000 toCurves in R2 Three descriptions (1) Graph of a function f R !R (That is y= f(x)) Such curves must pass the vertical line test Example When we talk about the \curve" y= x2, we actually mean to say the graph of the function f(x) = x2That is, we mean the set
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1 is often assessed by comparing it with thenull model, that re ects no dependence of y on the explanatory variables The model formula for the null model is > y ~ 1 signifying that we use a constant to approximate y The natural constant is the mean of y Functions in R that generate models report the statistics thatTtest(x, y = NULL, mu = 0, varequal = FALSE) arguments x A vector to compute the onesample ttest y A second vector to compute the two sample ttest mu Mean of the population varequal Specify if the variance of the two vectors are equal By default, set to `FALSE` Onesample ttestWe use the formula d = r * t, where d is the distance, r is the speed and t is time to solve the following problems Example 1 A car travels 1 miles at the speed of 48 miles per hour Find the time taken for the journey using the formula d = rt Solution Step 1 Distance, d = 1 miles;
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50 (298) Bilingual math tutor and much more See tutors like this See tutors like this I am assuming that you mean y= (14) t8 Using the laws of exponents, this equals 14 t * 14 8 This equals y = * (14) t By the way the number 4 is 40% Hope this helpedWhenever (t;y 1);(t;y 2) are in D L is Lipschitz constant I Example 1 f(t;y) = t y2 does not satisfy any Lipschitz condition on the regionFor t and r must be the same Example of Exponential Growth The 00 census found that a US Population of about 281 million with an estimated growth rate of 07% Q = Q0 x (1 r)t 4/1/10 2 Forms of the Exponential
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= 1 r Subtracting 1, you get that the rate is just over 003 or 3/10 of 1% The function that would model your growth is y = 484(1003)^t To do #2, find out how many years each year is after 1980, and plug those numbers in for "t" For example, to find 1985, you'd take 484(1003)^5 To do #3, "double" the original population would be 968 million peopleAs examples, y = x 3 4x C is the general solution of example a above, and y 1 = ½ x 2 C is the general solution of example b above, shown as the collection of red graphs below The collection of graphs of all particular solutions of a DE completely fill up space, and no two graphs overlap, much as the layers of a dagwood sandwichEXAMPLE 1 r(t)(4 t5)i tetj sin(4t)k (a) Find the derivative of (b) Find the unit tangent vector at the point t = 0 SOLUTION (a) According to this theorem, we differentiate each component of r r(t) = and r(o)j 4k, the unit tangent (b) Since r(0)= vector at the point (4, 0, 0) is j 4k
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FV = C 0 * (1 r)^5An equation for the depreciation of a car is given by y = A(1−r)t y = A (1 − r) t, where y = y = current value of the car, A = A = original cost, r = r = rate of depreciation, and t= t = time, inRewrite y=5(1/4)^{t/6} in the form y=a(1r)^t or y=a(1r)^t Round the value of r to the nearest tenthousandth Then tell whether the model represents exponential growth or exponential decay
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So jjjj mav= 2 >1 = jjAjj2 mav Remark Not all submultiplicative norms are induced norms An example is the FrobeniusTheory used in this question1 Method of charging (induction)https//youtube/drfZbYMf50k=====🔴 ELECTRIC CHARGES ANDY = a(1 r)t Example 1 Exponential Growth 1a) The prize for a radio station contest begins with a $100 gift card Once a day, a name is announced The person has 15 minutes to call or the prize increases by 25% for the next day Write an equation for the amount of the gift card in dollars after t days with no winners How much will the gift
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Y = a(1 r)t EXPONETIAL DECAY FUNCTION y = a(1 – r )t EXPONENTIAL DECAY APPLICATIONS 5 The population of a town is 2500 and is decreasing at a rate of 35% per year Write an exponential decay function to find the population of the town after 5 years EXPONENTIAL GROWTH APPLICATIONS 1The total work over some time periodExample 122 Solve y y 0 with given initial values y 0 y 0 Now ex and e x are solutions of this differential equation, so the general solution is a linear combination of these But we won't have as easy a time finding a solution like (123), since these functions do not have the initial values 1 0;
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FV = C 0 * (1 r) 1 * (1 r) 2 * * (1 r) T or FV = C 0 * (1 r)^T Where r is the interest rate, C 0 is the cash flow at time 0 (now), FV is the future value, and T is the number of periods Example Problem You are given $10,000 and you want to invest it in a 5 year CD that yields 4% interest per year How much money will you have in 5 years?Y = a(1 r)t Write exponential growth model = 609(1 )t Substitute 609 for a and for r = 609()t Simplify Using this model, you can estimate the world population in 05 (t = 5) to be y = 609()5 ≈ 646 billion b Use the table feature of a graphing calculator to determine that y ≈ 7 when t = 12 So, the world population was about 7 billion in 12S OLUTION Let y represent the purchasing power and let t = 0 represent the year 19 The initial amount is $1 Use an exponential decay model = ( 1 ) (1 – 0035 ) t = 0965 t y = C (1 – r ) t y = 0965 15 Exponential decay model Substitute 1 for C , 0035 for r Simplify
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